1 - The Cacafuego : - What happens when he finds itself on Treasure Island ? Given the battles between pirates players are not allowed , this boat requires a battle between players , as only the battles against the Legendary Pirates are allowed on this island ?

I peeled the forum French and English , but no exact answers were provided . What I found on the English forum:

1 - We do not care rule and kill players to win this boat.
2 - Not possible battles, this fashionable boat will move to the next island
3 - Given that there are no battles between players, all approach the boat and share the points.

So which option is right?

2 - The Royal Navy: Suppose that player 1 sinks this boat ... it takes the reward and we remove it from the board. Is this boat "may" come back later in the game with the second card , or permanently removed from the game? ie , player 1 could conceivably fight back against the Royal Navy ?

- Here I have not found answers in English or French forum (and I've spent hours searching )

The rules on page 13 in the section "Legendary Pirate battles with Multiple Players" apply here.

Normally, players must battle LP first before each other. Since on Treasure Island they only battle the LP. Since LP is Cacafuego, it is immediately defeated and spoils split among players there:

"If a Legendary Pirate is sunk, the fame value indicated on
its reference card is immediately split among all players present
who survive the combat. Fame points that cannot be distributed
evenly are rounded down to the nearest whole number.
Surviving players continue combat until only one player
ship remains."

The last sentence does not apply because the players are on Treasure Island.

Others have suggested house rules to make players fight for the Cacafuego, but you can house rule whatever you like. I prefer to follow the rules in this instance.

My understanding is that the Royal Navy can be brought in multiple times, once for each relevant Tavern card played, and unless you have your own miniature, the RN card represents the ship. After the battle, the "ship" is removed from the board, to be brought in again by another Tavern card. After all, the Royal Navy had many ships.

"The location of Treasure Island is a secret known only among pirates, therefore the Royal Navy will never be found sailing there."

While true and a good thing to point out here, in case there is a misunderstanding, I think the OP's question about Royal Navy is totally separate from the first question and a general question about battle with the RN.